Here’s the key to understanding the barn burner of a speech Bill Clinton just delivered. Senior Dems believe Clinton has taken on a unique role in American politics: They think he is seen by genuine undecided and swing voters as a kind of “referee” figure — someone they can trust to tell them what to think about politics and the economy. These voters, Dems believe, think he understands better than any other major figure exactly the kind of economy they want.

Clinton played that role with great gusto tonight, delivering a strong pitch for a second Obama term, combined with a sharp, point by point response to virtually every major GOP argument against him.

1) Clinton made the single strongest case we’ve heard for why undecided voters who are disappointed about the economy should give Obama another four years to finish what he started. He spoke directly to current voter disappointment by acknowledging they may not be feeling the recovery yet — but drew on his own credibility on the economy to urge them to have patience, telling them that before the Clinton economy took off, voters felt the same sense of skepticism and despair they do now. And he made a personal pitch to voters on this front, telling them he believes deeply that Obama has laid the foundation for a lasting recovery — and that changing course now invites disaster..

2) Clinton delivered a slashing indictment of GOP obstructionism during the Obama era in a fashion only he could pull off. He reminded voters of Mitch McConnell’s vow to make Obama a one term president, and then, in one of the big applause lines of the night, he said: “Senator, I hate to break it to you. But we’re going to keep President Obama on the job.”

But Clinton went further than this, casting this election as a referendum on whether cooperation itself can survive: “One of the main reasons America should re-elect President Obama is that he is still committed to cooperation.” This pitch was strongly geared towards independents who hate government gridlock, and Clinton’s stature and popularity with those independent voters — and that role as “referee” — is what enabled him to make such an aggressive case against one party to them.

3) Clinton rebutted every major Republican argument against Obama. He argued that Obama's approach to deficit reduction is far more balanced than that of Republicans — another key pitch to independents. He took on the claim that Obama looted Medicare to pay for Obamacare, ridiculing Paul Ryan, who has included the same savings in his own budget, as an almost buffoonish and hapless figure. He attacked Mitt Romney and Republicans for claiming Obama is gutting his — his own — welfare reform bill. And he offered an expansive defense of Obamacare, again drawing on his “referee” status to do so, frequently using phrases like: “Here’s what really happened.” Conclusion: “President Obama and the Democrats didn’t weaken Medicare, they strengthened it.”

Clinton recast this election as a clear choice between two sharply different versions of what has happened to our economy in recent years; two vastly different interpretations of what really happened during the Obama presidency; and two starkly different economic philosophies and road maps for the future. We’ll find out over time how many people actually watched the speech and how lasting its impact will be. But right now it looks plausible that Clinton’s unique role as “referee,” and the authority he has among the undecided voters Obama needs, may have enabled him to go some way towards redefining this race.